The 6563 Å Hα line emitted by hydrogen in a star is found to be redshifted by 15 Å. Estimate the speed with which the star is receding from the Earth. - Physics

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Numerical

The 6563 Å Hα line emitted by hydrogen in a star is found to be redshifted by 15 Å. Estimate the speed with which the star is receding from the Earth.

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Solution

Wavelength of `"H"_alpha` line emitted by hydrogen,

λ = 6563 Å

= 6563 × 10−10 m

Star’s red-shift, (λ' − λ) 15 Å = 15 × 10−10 m

Speed of light, c = 3 × 108 m/s

Let the velocity of the star receding away from the Earth be v.

The red shift is related with velocity as:

`lambda"'" - lambda = "v"/"c" lambda`

`"v" = "c"/lambda xx (lambda"'" - lambda)`

= `(3 xx 10^8 xx 15 xx 10^(-10))/(6563 xx 10^(-10))`

= 6.87 × 105 m/s

Therefore, the speed with which the star is receding away from the Earth is 6.87 × 105m/s.

Concept: Reflection and Refraction of Plane Wave at Plane Surface Using Huygens' Principle - The Doppler Effect
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Chapter 10: Wave Optics - Exercise [Page 384]

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NCERT Physics Class 12
Chapter 10 Wave Optics
Exercise | Q 10.11 | Page 384
NCERT Physics Class 12
Chapter 10 Wave Optics
Exercise | Q 11 | Page 384
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